Question

If (x-a) is the H.C.F of x^2-42x-343 and x^2+ax-98 then a is 1)7 2)-7 3)14 4)-14 plz tell which option is correct with explanation plz​

Answer 1

The value of a is -7. so the correct option is (2).

If (x - a) is the HCF of (x² - 42x - 343) and (x² + ax - 98).

We have to find the value of a.

It has given that (x - a) is the HCF of (x² - 42x - 343) and (x² + ax - 98). it means, (x - a) is a factor of both (x² - 42x - 343) and (x² + ax - 98).

We know, from Remainder theorem, If (x - k) is a factor of f(x) , then f(k) = 0.

∵ (x - a) is a factor of (x² + ax - 98).

∴ (a)² + a(a) - 98 = 0

⇒a² + a² = 98

⇒2a² = 98

⇒a² = 49

⇒a = 7 , -7

Also (x - a) is a factor of (x² - 42x - 343)

∴ (a)² - 42(a) - 343 = 0

⇒a² - 42a - 343 = 0

⇒a² + 7a - 49a - 343 = 0

⇒a(a + 7) - 49(a + 7) = 0

⇒(a - 49)(a + 7) = 0

⇒a = 49, -7

Here common value of a is -7 hence, the value of a is -7.